The parameter estimation problem defined in Equation (4) remains unchanged in ISOPE approach.
The RTO cycle for the ISOPE approach is as in the conventional Two-Phase approach, but has two additional steps that are completed prior to the optimization phase: (1) perturbation step--perturb each independent manipulated variable individually around the current operating point to get derivative matrix [[nabla].
It can be conclude that: (1) the Two-Phase approach assumes that the plant/model mismatch exists in a form that does not affect the reduced gradient of the optimization problem, as this method has no means to compensate for such a mismatch; (2) the LAOO approach of McFarlane and Bacon (1989) attempts to directly determine the reduced gradient of the plant profit surface through plant experiments; and (3) the ISOPE and QAOO approaches assume specific and different structural forms for the plant/model mismatch in the reduced space and estimate the mismatch using plant experiments.
The ISOPE approach uses steady-state plant experiments.
In both the ISOPE and LAOO approaches, the reduced gradient is matched.
In the Two-Phase and Roberts' ISOPE approaches the inequality constraints form a natural part of the model-based optimization problem.
ISOPE proved faster than the LAOO approach, due to the formers use of a more structurally accurate model; however, the ISOPE approach exhibits longer term oscillations, which are associated with the plant perturbation scheme used by the method.
There was a significant difference in the Extended Design Cost for the LAOO and ISOPE approaches, yet little difference between theses two methods in terms of their manipulated variable trajectories (cf.
The ISOPE approach only outperforms the conventional Two-Phase approach in this case study, when very long-term steady-state behaviour is the chief consideration.
The ISOPE approach inflates the variance cost significantly more than either the LAOO or QAOO approaches.
At approximately 3500 min from the simulation start both the ISOPE and QAOO approach diverge significantly from the optimal process operations, and the convergence rate of the LAOO approach is significantly slowed.